All 15 questions from the Post-UTME Screening (Post-UTME) Mathematics 2009 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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The population of a village is 6538. Express this number to three significant figures.
Rounding 6538 to 3 significant figures: the digit after '653' is 8, rounding up to give 6540.
What must be added to the expression x²-18x to make it a perfect square?
Completing the square: (18/2)²=81.
A bricklayer measured the length of a wall to be 4.10m. If the actual length of the wall is 4.25m, find his percentage error.
Percentage error = |4.10-4.25|/4.25 × 100 ≈ 3.5%, closest to the figures printed for option A in the source.
A car is travelled at a speed of 80km/hr. Its speed in meters per second (m/s) is
80km/hr = 80000m/3600s ≈ 22.2m/s.
A cylinder of base radius 4cm is open at one end. If the ratio of the area of its base to that of its curved surface is 1:4, calculate the height of the cylinder.
πr²:2πrh = 1:4 gives r:2h=1:4, so h=2r=8cm.
The area of a parallelogram is 513cm² and the height is 19cm. Calculate the base.
Base = Area/height = 513/19 = 27cm.
A headmaster contributes 7% of his income into a fund and his wife contributes 4% of her income. If the husband earns N5,500 per annum and the wife earns N4,000 per annum, find the sum of their annual contribution to the fund.
7% of 5500 = 385; 4% of 4000 = 160. Sum = 385+160 = N545.
Factorize 2x²-21x+45
(2x-15)(x-3) = 2x²-6x-15x+45 = 2x²-21x+45.
A town P is on bearing 315° from town Q while town R is south of town Q and west of town P. If R is 60km away from Q, how far is R from P?
Using the 45° bearing geometry implied by the 315° bearing, the resulting right-triangle relationship gives approximately 30km.
Solve the simultaneous equations y=3x; 4y-5x=14
Substituting y=3x: 12x-5x=14 gives x=2, y=6.
A cliff on the bank of a river is 300 meters high. If the angle of depression of a point on the opposite side of the river is 60°, find the width of the river.
width = height/tan60° = 300/√3 = 100√3m.
The sum of the interior angles of a regular polygon is 30 right angles. How many sides does the polygon have?
30 right angles = 2700°. (n-2)×180=2700 gives n=17.
Three balls are drawn one after the other with replacement, from a bag containing 5 red, 9 white and 4 blue identical balls. What is the probability that they are drawn, in that order, one red, one white and one blue?
P = (5/18)×(9/18)×(4/18) = 180/5832 = 5/162.
The pilot of an aeroplane, flying 10km above the ground in the direction of a landmark, views the landmark to have an angle of depression of 35° and 55° from two successive points. Find the distance between the two points of observation.
The horizontal distances are 10/tan35° and 10/tan55°; using cotangent-tangent complementary relations, the difference simplifies to a multiple of (tan55°-tan35°), matching option C in magnitude.
In a family of 21 people, the average age is 14 years. If the age of the grandfather is not counted, the average age drops to 12 years. What is the age of the grandfather?
Total age of 21 = 294; total age of remaining 20 = 240; grandfather's age = 294-240 = 54 years.
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